The failure of the diffusional description of the level crossing problem I. Violation of the von Neumann conditions.

Abstract

The validity of the kinetic equations describing a quantum system coupled to a classical bath was analyzed within the framework of a simple exactly solvable model. The equations were shown to violate the von Neumann conditions if the classical motion is strongly dependent on the state of the quantum system. 1 Introduction The electron transfer (ET) process in condensed media has been under intensive investigation for a few decades. Theoretically, it can be described by a radiationless transition in a quantum two-level system coupled to a large number of polarization modes of environment. The rate of electron transfer can be exactly calculated in two limiting cases. The first one corresponds to the weak coupling situation (nonadiabatic transfer). Accurate expression for the nonadiabatic transfer rate within the second order perturbation theory was found in the sixties [1-3]. The opposite adiabatic case has been successfully investigated more recently (see review [4] and reference herei..